Real-time coordinated operation of power and electric ride systems

ABSTRACT

A computer system for real-time coordinated operation of power distribution systems and electric vehicles accesses vehicle location information for one or more vehicles. Additionally, the system accesses charging station locations for one or more charging stations within a power distribution system. The computer system also accesses power distribution information describing voltage and/or current flow limits for the power distribution system. Further, the computer system routes a vehicle selected from the one or more vehicles to a first charging station location for charging, wherein the routing of the vehicle accounts for a current battery charge level of the vehicle and the power distribution information.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority to 1) U.S. Provisional Patent Application Ser. No. 63/389,594 filed on Jul. 15, 2022 and entitled “REAL-TIME COORDINATED OPERATION OF POWER AND AUTONOMOUS ELECTRIC RIDE-HAILING SYSTEMS,” and 2) U.S. Provisional Patent Application Ser. No. 63/394,818 filed on Aug. 3, 2022 and entitled “HIERARCHICAL COMBINATION OF ARTIFICIAL INTELLIGENCE AND OPTIMIZATION FOR THE OPERATION OF POWER SYSTEMS.” The entire contents of each of the aforementioned applications and/or patents are incorporated by reference herein in their entirety.

BACKGROUND

The potential for widespread public use of autonomous, or self-driving, vehicles has garnered extensive commercial and research interest. Some believe that if self-driving cars become widely adopted, the entire car ownership model may change. For instance, instead of personally owning one or more cars, individuals may instead hail an autonomous vehicle for a ride as needed. Such a system allows for the optimal usage of vehicles and road space, while potentially dramatically reducing parking needs in areas where real estate is at a premium.

Before a widely adopted self-driving car system can be utilized, a multitude of problems need to be addressed.

The subject matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one exemplary technology area where some embodiments described herein may be practiced.

BRIEF SUMMARY

Disclosed embodiments include a computer system for real-time coordinated operation of power distribution systems and electric vehicles. The computer system comprises one or more processors and one or more computer-readable media having stored thereon executable instructions that when executed by the one or more processors configure the computer system to perform various acts. For example the system may access vehicle location information for one or more vehicles. Additionally, the system may access charging station locations for one or more charging stations within a power distribution system. The computer system may also access power distribution information describing voltage and/or current flow limits for the power distribution system. Further, the computer system may route a vehicle selected from the one or more vehicles to a first charging station location for charging, wherein the routing of the vehicle accounts for a current battery charge level of the vehicle and the power distribution information.

This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

Additional features and advantages will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the teachings herein. Features and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. Features of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the manner in which the above-recited and other advantages and features can be obtained, a more particular description of the subject matter briefly described above will be rendered by reference to specific embodiments which are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments and are not therefore to be considered to be limiting in scope, embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings described below.

FIG. 1 illustrates a schematic of a computer system for real-time coordinated operation of power distribution systems and electric vehicles.

FIG. 2 illustrates a schematic of an example deep learning algorithm setup for training an agent.

FIG. 3 illustrates an action vector that is outside an example of a feasible diamond.

FIG. 4 illustrates a flow chart of steps in a method for real-time coordinated operation of power distribution systems and electric vehicles.

DETAILED DESCRIPTION

Disclosed embodiments include computer systems and computer-implement methods for optimizing electric vehicle charging based upon locations of the vehicles, locations of charging stations, and the associated power distribution systems (PDS). One of skill in the art will appreciate that as a greater number of vehicles transition to electric drivetrains, there will be an associated increased demand on PDS. This increased demand may be reflected in increased rates for charging at particular times and/or locations, increased instability in PDS, and various other negative outcomes.

Accordingly, disclosed embodiments are directed towards providing a system for routing electric vehicles (AEV), both autonomous and human-driven, to optimal charging stations based upon one or more of the following: the battery levels of the vehicle, the location of the vehicle, the location of charging stations, and/or characteristics of the associated power distribution system. As such, in at least one embodiment, the system may not route a vehicle to the nearest charging station, but instead route a car to a charging station that is associated with better power distribution system attributes. As used herein, the power distribution system attributes may comprise one or more of the following: power balance at different nodes within the power distribution system, power cost at different nodes within the PDS, energy stability at different nodes within the PDS, amperage at different nodes within the PDS, and various other related attributes.

In at least one embodiment, a computer system 100 for real-time coordinated operation of power and autonomous electric ride-hailing systems comprises one or more processors and one or more computer-readable media having stored thereon executable instructions that when executed by the one or more processors configure the computer system to perform various methods. The computer system 100 may execute a vehicle and PDS optimization software application 130. The software application 130 is configured to execute instructions in accordance with embodiments described herein.

The computer system 100 may access vehicle location information for one or more vehicles using the vehicle location process 140. The vehicle location process 140 may track a location of one or more vehicles using location tracking technology, such as GPS. The vehicle location process 140 may also utilize the map database 144 to identify the vehicles location on a map and/or to identify driving routes for the vehicles. Additionally, in at least one embodiment, the vehicle location process 140 may also track locations of passengers for an autonomous electric ride-hailing system. The computer system 100 may account for the location of passengers when identifying optimal charging stations. For example, the computer system 100 may direct the electric vehicle to charging stations that are along the route to picking up the passengers.

As used herein, a “process” comprises computer executable code and/or computer hardware that performs a particular function. One of skill in the art will appreciate that the distinction between different processes is at least in part arbitrary and that processes may be otherwise combined (e.g., into a single thread) and divided (e.g., into multiple threads) and still remain within the scope of the present disclosure. As such, the description of a component as being a “process” is provided only for the sake of clarity and explanation and should not be interpreted to indicate that any particular structure of computer executable code and/or computer hardware is required, unless expressly stated otherwise. In this description, the terms “module,” “component”, “agent”, “manager”, “service”, “engine”, “virtual machine” or the like may also similarly be used.

The computer system 100 also accesses charging station locations for one or more charging stations within a power distribution system using the charging station tracking process 142. The charging station tracking process 142 may be configured to track the location of charging stations using the map database 144. Further, the charging station tracking process 142 may also track queues at charging stations and/or general availability at charging stations. For example, the charging station tracking process 142 may identify that one or more charging stations are out of operation. Similarly, the charging station tracking process 142 may identify that a particular charging station has a queue of multiple cars waiting to charge.

The computer system 100 may further access power distribution information describing voltage and/or current flow limits for the power distribution system using the PDS tracking process 146. The power distribution information comprises power distribution system attributes described above. In at least one embodiment, the PDS tracking process utilizes information in the map database 144 to identify the locations of various nodes and lines within the PDS. In particular, the PDS tracking process 146 may map the location of various nodes and lines to roads, charging stations, and locations of electric vehicles. Additionally, the PDS tracking process may utilize an API to communicate directly with the PDS or sensors distributed through the PDS in order to gather power distribution information.

The computer system 100 may then route a vehicle selected from the one or more vehicles to a first charging station location for charging. In at least one embodiment, routing of the vehicle accounts for a current battery charge level of the vehicle and the power distribution information using the vehicle location process 140. Additionally, in at least one embodiment, routing the vehicle also accounts for traffic data. For example, the optimal charging station may at least in part depend upon current traffic levels. For instance, in heavy traffic an electric car may not have sufficient battery charge left to reach a particular optimal charging station, as such, the electric car may be routed to another optimal charging station. As will be explained in additional detail below, the computer system may account for power distribution information when selecting an optimal charging station.

In at least one embodiment, the computer system 100 is configured to display a map, on a computer interface, wherein the map comprises a visual indication of a route to the first charging station location. For example, the computer system 100 may communicate map information to a user interface within an electric car. The user interface may comprise a screen mounted within the electric vehicle. A driver in the electric car may be able to follow directions to an optimal charging station selected by the computer system 100. Further, the computer system 100 may also be able to notify a user when the user should begin driving to a particular charging station. For instance, the computer system 100 may identify both an optimal charging station and an optimal charging time based upon at least the electric vehicle's battery level and the power distribution information.

Additionally or alternatively, the computer system 100 may communicate routing information to an AEV. The routing information may cause the AEV to automatically begin driving to the optimal charging station provided by the computer system 100. The computer system may model the AEVs and PDS with two interdependent graphs to capture the intertwined structure and cascading constraints between the two operating systems. The AEVs charge their batteries at charging stations throughout the transportation system and draw power from the PDS. In this setting, the PDS constraints enable the AEVs operator to schedule the AEVs charging sessions such that deliverability of charging power is ensured in real-time operation. In some embodiments, a passenger within the AEV or a remote administrator for the AEV may need to first agree to allow the AEV to travel to the optimal charging station.

Optimal operation of a power distribution system requires solving a combinatorial optimization problem over a time horizon, and is often subject to uncertainties due to consumer behavior, renewable generation, and equipment failure. Stochastic optimization and model predictive control are well-established methods to tackle this optimization problem. Despite its effectiveness in solving traditional operational problems, mathematical programming struggles in highly uncertain or high-dimensional environments. For instance, stochastic optimization deals with operational uncertainties by solving a model over a limited number of select scenarios, which limits the observability over countless possibilities. Moreover, operation of numerous Distributed Energy Resources (DER), even by distributed and decomposed optimization techniques, requires a computational power that increases at least linear with the number of decision variables, which can be expensive for real-time operation of large networks. On the other hand, in at least one embodiment, the capabilities of Deep Reinforcement Learning (DRL) in solving stochastic and high dimensional problems may provide a fast and scalable alternative for solving large-scale operational problems.

In DRL, infeasible or unsafe solutions are typically avoided by adding a penalty factor during training, or clipping the solution within its direct limits, however, none of them ensure that all constraints are met when a deep neural network (NN) is used as a black box. The verification problem is even more troublesome when an NN is trained within unsupervised frameworks such as DRL, where using adversary examples in the training is not as effective in correcting their behavior. One approach to tackle this problem is to form a feasibility set to compare the operational solutions with and to identify the ones that are not proven to be feasible, and bypassing the DRL agent in those states. However, it does not offer an alternative operational decision, if the solution is not feasible. For DRL to be a practical tool in operational problem, a feasibility assurance is required, such that in any system state a solution is offered by DRL that satisfies all system constraints. In at least one embodiment, a solution is provided by finding the largest feasibility convex space of the power system variables, before training a DRL agent for operation.

In at least one embodiment, first, the operation of power distribution system with numerous DER is formulated as a Markov Decision Process (MDP), and a DRL agent is trained by a Deep Deterministic Policy Gradient (DDPG) to make decision on DER power dispatch. A convex feasible region in the form of a diamond-shaped multi-dimensional polyhedron, named a feasibility diamond, is then formed in the DRL decision space. This convex feasibility region is formed by finding a center in the decision space that satisfies all constraints, and moving from the center in the dimension of each decision variable k∈{1, . . . , K} with distance R k still results in a feasible decision. The center for which the volume of diamond with semi-axes R=[R 1, . . . , R K] is maximum, serves as the center of the largest feasibility diamond. The resulting diamond is the certified feasible region that guarantees feasibility inside, and can be used to find the projection of infeasible points on the feasible region.

Disclosed embodiments may include a convex feasibility region that is formed in the form of a diamond-shape polyhedron for the action space of the distribution system, which guarantees feasibility inside given a convex optimization model. The feasibility diamond is used for quick feasibility check of DRL solutions. Additionally, disclosed embodiments may include for any DRL solution outside the diamond, its projection on the diamond's surface is taken as the closest feasible point and used to modify the exploration process. Disclosed embodiments may also include the optimality criterion of DRL is also transformed by calculating the distance of infeasible points from the feasibility diamond and penalizing it in the long-term reward function. Further, disclosed embodiments may include the impact of modifying exploration process and optimality criterion, individually and combined, are investigated in three test distribution systems, indicating that feasibility is only guaranteed by modifying the exploration process. However, modifying the optimality criterion by adding a small penalization term for infeasibilities, which should be tuned for each distribution system, improves the optimality of solutions.

In at least one embodiment, a power distribution system can be represented by a graph (

,

), where i∈

represents each node, and line sections are denoted by (i, j) ∈

. Let p_(i) ^(L), q_(i) ^(L) of denote installed active and reactive power demand on each node, and y_(i) denote the loading factor. Active and reactive power flow in each line section are shown by p_(ij), q_(ij) respectively, and v_(i)=V_(i) ² denotes the squared voltage of each node. There are also a subset of nodes

_(G)⊂

where power generation units reside, and their active and reactive generations are denoted by p_(i) ^(g), q_(i) ^(g). The general notation

_(G) is used for all power generation units, including DGs, substation bus, and ESS units (for which p_(i) ^(g) can also be negative), however,

_(E)⊂

_(G) denotes only ESS units. Distribution system operation is governed by the following branch flow equations which are inherently non-linear and non-convex:

$\begin{matrix} {{{{\sum\limits_{{j❘{({i,j})}} \in \mathcal{L}}p_{ij}} - p_{ji} + \frac{r_{ij}\left( {p_{ji}^{2} + q_{ji}^{2}} \right)}{\nu_{i}}} = {p_{i}^{\mathcal{g}} - {y_{i}p_{i}^{L}}}},{\forall i}} & {{Equation}1} \end{matrix}$ $\begin{matrix} {{{{\sum\limits_{{j❘{({i,j})}} \in \mathcal{L}}q_{ij}} - q_{ji} + \frac{x_{ij}\left( {q_{ji}^{2} + q_{ji}^{2}} \right)}{\nu_{i}}} = {q_{i}^{\mathcal{g}} - {y_{i}q_{i}^{L}}}},{\forall i}} & {{Equation}2} \end{matrix}$ $\begin{matrix} {{\nu_{i} = {\nu_{j} - {2\left( {{r_{ij}p_{ij}} + {x_{ij}q_{ij}}} \right)} + {\left( {r_{ij}^{2} + x_{ij}^{2}} \right)\frac{r_{ij}\left( {p_{ji}^{2} + q_{ji}^{2}} \right)}{\nu_{i}}}}},\ {\forall i},j} & {{Equation}3} \end{matrix}$

where Equation 1 and Equation 2 represent power balance on each node, and Equation 3 governs voltage drop across each distribution line. This non-convex model needs a convex approximation to stay tractable for distribution systems of any size. Various convex approximations of branch flow has been suggested in the literature; for instance, setting v_(i)≈1 in Equation 1 and Equation 2 and ignoring the last high-order term in Equation 3 results in a quadratic model, which is widely used in power system studies. That model can also turn into a linear one if the quadratic power loss terms in Equation 1 and Equation 2 are ignored. These linear approximations would introduce 1-5% modeling error, however, the constraints may be tightened slightly to account for the error. Linear modeling, adopted in this work, allows for using only a half matrix of p_(ij), q_(ij) by setting p_(ij)=−p_(ij) and representing power flow equations in the matrix form. In distribution systems with high DER penetration, the operation is typically optimized with the objective of minimizing the cost of power acquisition from all resources, shown by C, subject to branch flow equations and constraints on voltage, line flow, DG generation, and ESS storage limits:

$\begin{matrix} {{\underset{s.t.}{\min\limits_{p^{\mathcal{g}},q^{\mathcal{g}}}}C} = {1^{\top}\lambda^{\mathcal{g}}p^{\mathcal{g}}}} & {{Equation}4} \end{matrix}$ $\begin{matrix} {{p^{\mathcal{g}} - {y \cdot p^{L}}} = {I^{M} \times p}} & {{Equation}5} \end{matrix}$ $\begin{matrix} {{q^{\mathcal{g}} - {y \cdot q^{L}}} = {I^{M} \times q}} & {{Equation}6} \end{matrix}$ $\begin{matrix} {{\Delta v} = {{{- 2}{r.p}} - {2{x.q}}}} & {{Equation}7} \end{matrix}$ $\begin{matrix} {\underset{¯}{v} \leq v \leq \overset{¯}{v}} & {{Equation}8} \end{matrix}$ $\begin{matrix} {{p^{2} + q^{2}} \leq \left( {\overset{¯}{s}}^{l} \right)^{2}} & {{Equation}9} \end{matrix}$ $\begin{matrix} {{p^{\mathcal{g}2} + q^{\mathcal{g}2}} \leq \left( {\overset{¯}{s}}^{\mathcal{g}} \right)^{2}} & {{Equation}10} \end{matrix}$ $\begin{matrix} {{E = {E^{- 1} - {\eta p^{\mathcal{g}}}}},{p^{\mathcal{g}} = \left\{ p_{i}^{\mathcal{g}} \right\}},{\forall{i \in \mathcal{N}_{E}}}} & {{Equation}11} \end{matrix}$ $\begin{matrix} {\underset{¯}{E} \leq E \leq \overset{¯}{E}} & {{Equation}12} \end{matrix}$

where λ^(g) is the generation cost vector. In this study, vectors and matrices are denoted by bold letters; for instance p, p^(g) represent the vectors of all p_(ij), p_(i) ^(g), respectively. Equation 4-Equation 6 are linear approximation of Equation 1-Equation 3 in the matrix form, where I^(M) is the nodeline incidence matrix and (.) operation is element-wise matrix multiplication. Also, node voltages, line flows and DER outputs are limited by Equation 7-Equation 9, where s^(l) and s^(g) represent the apparent power in lines and DG outputs, respectively. Finally, the evolution of ESS state of charge is given by Equation 10, where E, E⁻¹ are the current and previous state of charge, and η is the charging efficiency.

In order to train a DRL agent for distribution system operation, the operation problem may be reformulated as a Markov Decision Process (MDP) to be compatible with DRL framework. An MDP refers to decision-making in an environment, where conditions at any time are represented by the matrix of system states, based on which a decision is made and that results in a reward and transition to a new state. The state transition is governed by a probabilistic transition function that is defined by system structure and uncertainty sources. The following MDP components to reformulate the problem of operating DER in a distribution system are defined as follows:

System state: denoted by s∈

S represents variable system conditions. Real-time energy price (λ^(g)), loading factor (y), availability of distribution lines (e), and energy reserve of ESS units (E) are typical system state parameters. Any additional data that affect the operation, including time coordinates (e.g., time of the day, day of the week, seasonal changes), weather data, and predicted values for load and renewable generation may be included in the system state as well. The system state is defined as s=[λ^(g), y, E, e, X], where X represents any additional data.

Actions: denoted by u∈

includes operational decisions or control variables in grid operation. While a wide range of variables may be directly controlled by the operator, disclosed embodiments focus on operation of DER and define the action space as their active and reactive power generation vectors, u=[p^(g), q^(g)]. Note that reactive generation, q^(g) may also be excluded from control variables if it is not dispatched directly and its value is determined based on loading condition and power generation capacity of DER units.

Reward: denoted by r(s, u):

×

→

is the reward of taking action u in state s.

The reward value is defined as the change in operation cost, given by:

r(s,u)=C(s,u)−C(s,0)−M∥u∥   Equation 13

where the first and second terms are operation costs with and without taking action u. Also, the last term is a regularization term that penalizes the size of the action with factor M and helps with avoiding unnecessary large actions. Note that the cost value C is obtained by solving Equation 11 with fixed state and actions, which results in a unique C value.

Transition function: denoted by p(s′|s, u):

×

×

→[0, 1] specifies the probability of transitioning between system states, given a certain action is taken. Note that in stochastic operation, the transition function is hard to obtain and DRL does not directly use it but learns it through numerous observation of transitions.

The objective of DRL is to find an action policy n(s)=u that results in the highest long-term reward, over all possible state transitions. More specifically DRL tries to solve the following problem:

$\begin{matrix} {\max\limits_{u_{t} \in U}{{\mathbb{E}}_{\sim{p({{s_{t + 1}❘s_{t}},u_{t}})}}\left\lbrack {\sum\limits_{t = t_{0}}^{\infty}{\gamma^{t}\left\lbrack {r\left( {s_{t},u_{t}} \right)} \right\rbrack}} \right\rbrack}} & {{Equation}14} \end{matrix}$

where the reward is maximized over a large number of time steps t and γ is the discount factor that signifies the importance of immediate versus long-term rewards in decisionmaking. DRL solves this problem by assigning a Q-value to each pair of state and action, indicating the long-term value of the action. Q-values are initialized randomly, but during the training procedure, they are updated using the following recursive equation, also known as the Bellman equation, to get closer to their actual values:

$\begin{matrix} {{Q\left( {s,u} \right)} = {{r\left( {s,u} \right)} + {{\gamma\mathbb{E}}_{\sim{p({{s^{\prime}❘s},u})}}\left\lbrack {\max\limits_{u^{\prime} \in U}{Q\left( {s^{\prime},u^{\prime}} \right)}} \right\rbrack}}} & {{Equation}15} \end{matrix}$

In the recursive equation above, state and action of the current step (s_(t), u_(t)) are shown by (s, u), while state and action of the next step (s_(t+1),u_(t+1)) are denoted by (s′, u′). In distribution system operation, state parameters are continuous and the number of possible state-action pairs are unlimited; therefore, Q-values are estimated using neural networks trained on a limited number of state-action samples. Since actions are also from a continuous space, we use Deep Deterministic Policy Gradient (DDPG) method which is capable of handling continuous actions in DRL. DDPG utilizes two neural networks, namely actor and critic, to make and evaluate actions, respectively. The actor network takes the system state as input and makes a decision μ(s;θ^(μ)), where θ^(μ) is the actor's weight vector. Therefore, its input and output layers are the same size as the states and action vectors. Decision μ, the power dispatch of DER units, must be selected within power capacity of the unit, and in case of ESS, must meet the ESS constraints. Therefore, initial decision μ(s; θ^(μ))=[p^(g), q^(g)] is modified in the following order:

p ^(g)=max{ p ^(g),min{p ^(g) ,p ^(g)}}   Equation 16

p _(i) ^(g)=min{p _(i) ^(g) ,ηE _(i) ⁻¹ },∀i∈

_(E)   Equation 17

p _(i) ^(g)=max{p _(i) ^(g)(1/η)(E _(i) ⁻¹ −Ē _(i))},∀i∈

_(E)   Equation 18

|q ^(g)|=min{|q ^(g)|,√{square root over (s ^(g) −p ^(g))}}   Equation 19

In equations above, DER active and reactive generations are limited in Equation 15, Equation 18, and constraints Equation 16, Equation 17 ensure that energy storage constraints of ESS units are met when discharging and charging, respectively. The state of charge of ESS units are updated once all actions are taken and their feasibilities are confirmed.

The critic network takes the system state and the action taken by the actor as input and estimates the Q-value of the taken action as Q(s, u; θ^(Q)). Therefore, its input layer has the same size as state and action vectors added together, and the output layer has the same size as the action vector. Also, to stabilize the training process, in each training iteration, a batch of N training samples are randomly chosen from B previous steps, stored in a replay memory, and is used to update the critic networks using a gradient descent step as follows:

$\begin{matrix} {\theta^{Q} = {\theta^{Q} - {\alpha^{Q}{\nabla_{\theta Q}{L\left( \theta^{Q} \right)}}}}} & {{Equation}20} \end{matrix}$ $\begin{matrix} {{L\left( \theta^{\Theta} \right)} = {\frac{1}{N}{\sum\limits_{n}\left( {{Q\left( {s,{{\mu\left( {s;\theta^{\mu}} \right)};\theta^{Q}}} \right)} - \Gamma_{i}} \right)^{2}}}} & {{Equation}21} \end{matrix}$ $\begin{matrix} {\Gamma_{i} = {{r\left( {s,{\mu\left( {s;\theta^{\mu}} \right)}} \right)} + {Q\left( {s^{\prime},{{\mu\left( {s^{\prime};\theta^{\mu}} \right)};\theta^{Q}}} \right)}}} & {{Equation}22} \end{matrix}$

The actor network is updated to make a decision with the maximum of the estimated Q-value, and therefore takes a gradient ascent step as follows:

$\begin{matrix} {\theta^{\mu} = {\theta^{\mu} - {\alpha^{\mu}{\nabla_{\theta^{\mu}}{Q\left( {s,{u;\theta^{Q}}} \right)}}}}} & {{Equation}23} \end{matrix}$ $\begin{matrix} {{\nabla_{\theta^{\mu}}{Q\left( {s,{u;\theta^{Q}}} \right)}} = {\frac{1}{N}{\sum\limits_{n}{{\nabla_{u}{Q\left( {s,{u;\theta^{Q}}} \right)}} \cdot {\nabla_{\theta^{\mu}}{\mu\left( {s;\theta^{\mu}} \right)}}}}}} & {{Equation}24} \end{matrix}$

In each training step, the actor network output μ(s, u) which is the vector of decided actions for DER power dispatch is clipped within the upper and lower bounds of DER generation, before using it to update the networks. Also, a random noise is added to the action, to avoid overfitting during training. Note that stabilizing techniques such as using target networks are also applied in training DRL agents. The training procedure is shown in FIG. 2 , highlighting the position of replay memory in the training procedure. In the depicted schematic 100, p^(g) and q^(g) are fixed to the action values u as indicated in Equations 4-12. The trained actor network is detached from the training setup and used directly for decision making in a power distribution system. However, the trained agent may take actions that violate power flow constraints, including power balance, voltage limitations, or power capacity of lines. In the next section, we address this issue by a finding feasibility diamond that allows for verifying the feasibility of DRL solutions and modifying infeasible ones.

At least one embodiment is configured to find the largest convex region in the DRL action space, where all distribution system constraints are met, should any action is taken from that space. For a given generation input vector u=[p^(g), q^(g)] and an initial condition y, branch flow equations determine power system state variables X=[v, p, q], which should be within their upper and lower bounds. The state vector may be expressed as a linear function of inputs and initial conditions as X=

(u, v). The objective here is to find a feasibility set

over (u, y), for which X is guaranteed to be in the safe region

(X). In other words, a feasibility set

is desired for which ∀(u, y) ∈

→

(u, v)=X∈

(X).

Forming a feasibility set in the form of a diamond-shaped polyhedron, called feasibility diamond hereafter, has two advantages when verifying operational actions; first, it is easy and quick to check if actions are inside the diamond, and second, if the input vector is outside the feasible region, its projection on the diamond's surface may be found and used as the closest feasible action. The feasibility diamond is formed in space P:

×

with center P⁰ and semi-axes R_(k) in every dimension k∈{1, . . . , K} of P, and contains values of u, y for which the resulting state X is guaranteed to be feasible. To illustrate how this diamond is formed, let us assume a power system with N^(g) generation units and N independent loads, and K=N^(g)+N. The diamond must satisfy two conditions to be feasible all around; first, the center P⁰=[p₁ ^(g), . . . , p_(N) _(g) ^(g), q₁ ^(g), . . . , q_(N) _(g) ^(g), y₁, . . . , y_(N)]^(T) should result in a feasible state, i.e., X⁽⁰⁾=

(P⁰)∈

(X). Second, by moving along semi-axis k∈K with distance R_(k), a new point is reached that also results in a feasible state. The new point is a vertex of the feasibility diamond. Given a convex power flow model, the feasibility of all points inside such polyhedron may be stated that if all vertices of a k-dimensional polyhedron in the input space of a convex system are feasible, then the whole space enclosed by the polyhedron is also feasible.

Given that DRL is deciding on the output of DER units, an action vector û is decided in initial condition y. Note that the initial condition y is not controlled by the operator, and the input vector is the only controllable operational variable. If the action vector is outside the feasible diamond 200, its projection on the diamond's surface can be taken as the closest point with guaranteed feasibility, as shown in FIG. 3 .

In at least one embodiment, such a projection can be found as indicated below: Let diamond ε:

${\frac{❘{x_{1} - x_{1}^{c}}❘}{R_{1}} + \frac{❘{x_{2} - x_{2}^{c}}❘}{R_{2}} + \cdots + \frac{❘{x_{n} - x_{n}^{c}}❘}{R_{n}}} \leq 1$

be centered at x^(C) with semi-axes vector R, {circumflex over (x)}=[{circumflex over (x)}₁, {circumflex over (x)}₂, . . . , {circumflex over (x)}_(n)] be a point outside ε. The projection of {circumflex over (x)} on the surface of ε is given by:

$\begin{matrix} {x^{proj} = \left\lbrack {{{a_{1}t} + x_{1}^{c}},{{a_{2}t} + x_{2}^{c}},\ldots,{{a_{n}t} + x_{n}^{c}}} \right\rbrack} & {{Equation}25} \end{matrix}$ $\begin{matrix} {{r = \frac{{sign}\left( {{\overset{\hat{}}{x}}_{1} - x_{1}^{c}} \right)}{\sum_{i = 1}^{n}\frac{❘a_{i}❘}{R_{i}}}},{a_{i} = \frac{{\overset{\hat{}}{x}}_{i} - x_{i}^{c}}{{\overset{\hat{}}{x}}_{1} - x_{1}^{c}}},{{\forall i} = \left\{ {1,\ldots,n} \right\}}} & {{Equation}26} \end{matrix}$

In the standard DRL, the actor network is solely guided by the reward function, which is typically aligned with the problem's objective. For the DRL agent to avoid the infeasible region, infeasible actions can be penalized in the reward function. More specifically, infeasible actions receive a negative reward proportional to their distance from the feasible region. Since we have already obtained the projection of a potentially infeasible point on the diamond's surface, the infeasibility value can be associated with the distance d to such a projection, given by d^(u)=|u−u^(proj)|. Therefore, the reward function (5.3) will be re-written as:

r(s,u)=C(s,u)−C(s,0)−M∥u∥ _(m) −w×d ^(u)   Equation 27

The penalization factor w must be tuned carefully, because it can adversely affect the DRL solution. In DRL training, actor network is trained using the loss function in Equations 19-21. which includes the reward function and, therefore, the penalization of infeasibilities. If the penalization factor w is too large, then even a slight violation beyond border points would result in a large loss function and subsequently a drastic change in network weights that pushes actions away from border points, where the optimal solutions generally reside.

Let us assume decision making in an action space, where action 0 is close to the border. Due to explorative nature of DRL, after one training iteration the new action could be on the other side of the border (action 1). A large penalty for this violation results in a large loss function in the next training iteration, which shift actions considerably in a direction that reduces loss (towards action 2). However, a softer penalization, while pushing actions towards the feasible region, does not shift them dramatically, allowing for more exploration of border points (action 2′). Tuning parameter w for efficient modification of the optimality criterion is studied in the next section.

In at least one embodiment, the feasibility of solutions given by a DRL-trained distribution system operation model is checked against a convex feasibility region in the form of a diamond-shaped polyhedron, formed inside the region defined by constraint hyperplanes of the operation model. The feasibility diamond is formed by finding a center that satisfies system constraints and by moving in each dimension from the center to the diamond's surface, the constraints are still satisfied. The polyhedron is used for a quick feasibility check of any solution given by DRL, and allows for modifying the exploration process by finding the projection of infeasible solutions on the diamond's surface. Further, the distance between the infeasible action and its projection on the diamond is used to modify the optimality criterion and penalizing infeasibilities in the DRL training. While modifying the exploration process eliminates the chance of infeasible solutions, a soft penalization of infeasibilities can improve the final solutions in terms of optimality. The optimal value of the penalization coefficient depends on the grid size and configuration, and must be optimized for each case. However, in all studies, strong penalization of infeasibilities overshadows other components of the long-term reward and results in conservative actions that deteriorate the optimality of the final solution.

The following discussion now refers to a number of methods and method acts that may be performed. Although the method acts may be discussed in a certain order or illustrated in a flow chart as occurring in a particular order, no particular ordering is required unless specifically stated, or required because an act is dependent on another act being completed prior to the act being performed.

FIG. 4 depicts a flow chart of steps in a method 400 for real-time coordinated operation of power distribution systems and electric vehicles. The method 400 includes a step 410 of accessing vehicle location information for one or more vehicles. For example, the vehicle location process 140 can track vehicle location using a system, such as GPS. Method 400 also includes a step 420 of accessing charging station locations for one or more charging stations within a power distribution system. For example, the charging station tracking process 142 can track charging station locations and also access information relating to the status of a given charging station.

Additionally, method 400 may include a step 430 of accessing power distribution information describing voltage and/or current flow limits for the power distribution system. For example, the PDS tracking process 146 may access information relating to current PDS characteristics. Further, the method 400 may include a step 440 of routing a vehicle selected from the one or more vehicles to a first charging station location for charging, wherein the routing of the vehicle accounts for a current battery charge level of the vehicle and the power distribution information. For example, the vehicle location process 140 may utilize information within the map database 144 to direct the vehicle to an optimal charging station.

Further, the methods may be practiced by a computer system including one or more processors and computer-readable media such as computer memory. In particular, the computer memory may store computer-executable instructions that when executed by one or more processors cause various functions to be performed, such as the acts recited in the embodiments.

Computing system functionality can be enhanced by a computing systems' ability to be interconnected to other computing systems via network connections. Network connections may include, but are not limited to, connections via wired or wireless Ethernet, cellular connections, or even computer to computer connections through serial, parallel, USB, or other connections. The connections allow a computing system to access services at other computing systems and to quickly and efficiently receive application data from other computing systems.

Interconnection of computing systems has facilitated distributed computing systems, such as so-called “cloud” computing systems. In this description, “cloud computing” may be systems or resources for enabling ubiquitous, convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, servers, storage, applications, services, etc.) that can be provisioned and released with reduced management effort or service provider interaction. A cloud model can be composed of various characteristics (e.g., on-demand self-service, broad network access, resource pooling, rapid elasticity, measured service, etc.), service models (e.g., Software as a Service (“SaaS”), Platform as a Service (“PaaS”), Infrastructure as a Service (“IaaS”), and deployment models (e.g., private cloud, community cloud, public cloud, hybrid cloud, etc.).

Cloud and remote based service applications are prevalent. Such applications are hosted on public and private remote systems such as clouds and usually offer a set of web based services for communicating back and forth with clients.

Many computers are intended to be used by direct user interaction with the computer. As such, computers have input hardware and software user interfaces to facilitate user interaction. For example, a modern general purpose computer may include a keyboard, mouse, touchpad, camera, etc. for allowing a user to input data into the computer. In addition, various software user interfaces may be available.

Examples of software user interfaces include graphical user interfaces, text command line based user interface, function key or hot key user interfaces, and the like.

Disclosed embodiments may comprise or utilize a special purpose or general-purpose computer including computer hardware, as discussed in greater detail below. Disclosed embodiments also include physical and other computer-readable media for carrying or storing computer-executable instructions and/or data structures. Such computer-readable media can be any available media that can be accessed by a general purpose or special purpose computer system. Computer-readable media that store computer-executable instructions are physical storage media. Computer-readable media that carry computer-executable instructions are transmission media. Thus, by way of example, and not limitation, embodiments of the invention can comprise at least two distinctly different kinds of computer-readable media: physical computer-readable storage media and transmission computer-readable media.

Physical computer-readable storage media includes RAM, ROM, EEPROM, CD-ROM or other optical disk storage (such as CDs, DVDs, etc.), magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer.

A “network” is defined as one or more data links that enable the transport of electronic data between computer systems and/or modules and/or other electronic devices. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a computer, the computer properly views the connection as a transmission medium.

Transmissions media can include a network and/or data links which can be used to carry program code in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer. Combinations of the above are also included within the scope of computer-readable media.

Further, upon reaching various computer system components, program code means in the form of computer-executable instructions or data structures can be transferred automatically from transmission computer-readable media to physical computer-readable storage media (or vice versa). For example, computer-executable instructions or data structures received over a network or data link can be buffered in RAM within a network interface module (e.g., a “NIC”), and then eventually transferred to computer system RAM and/or to less volatile computer-readable physical storage media at a computer system. Thus, computer-readable physical storage media can be included in computer system components that also (or even primarily) utilize transmission media.

Computer-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. The computer-executable instructions may be, for example, binaries, intermediate format instructions such as assembly language, or even source code. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the described features or acts described above. Rather, the described features and acts are disclosed as example forms of implementing the claims.

Those skilled in the art will appreciate that the invention may be practiced in network computing environments with many types of computer system configurations, including, personal computers, desktop computers, laptop computers, message processors, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, mobile telephones, PDAs, pagers, routers, switches, and the like. The invention may also be practiced in distributed system environments where local and remote computer systems, which are linked (either by hardwired data links, wireless data links, or by a combination of hardwired and wireless data links) through a network, both perform tasks. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

Alternatively, or in addition, the functionality described herein can be performed, at least in part, by one or more hardware logic components. For example, and without limitation, illustrative types of hardware logic components that can be used include Field-programmable Gate Arrays (FPGAs), Program-specific Integrated Circuits (ASICs), Program-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), etc.

The present invention may be embodied in other specific forms without departing from its spirit or characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope. 

What is claimed is:
 1. A computer system for real-time coordinated operation of power distribution systems and electric vehicles, comprising: one or more processors; and one or more computer-readable media having stored thereon executable instructions that when executed by the one or more processors configure the computer system to: access vehicle location information for one or more vehicles; access charging station locations for one or more charging stations within a power distribution system; access power distribution information describing voltage and/or current flow limits for the power distribution system; and route a vehicle selected from the one or more vehicles to a first charging station location for charging, wherein the routing of the vehicle accounts for a current battery charge level of the vehicle and the power distribution information.
 2. The computer system as recited in claim 1, wherein the executable instructions include instructions that are executable to configure the computer system to display a map, on a computer interface, wherein the map comprises a visual indication of a route to the first charging station location.
 3. The computer system as recited in claim 1, wherein the vehicle location information and the power distribution system are modelled with two interdependent graphs.
 4. The computer system as recited in claim 1, wherein at least one of the one or more vehicles comprises an autonomous electric vehicle.
 5. The computer system as recited in claim 4, wherein the executable instructions for routing the vehicle selected from the one or more vehicles to the first charging station location for charging further include instructions that are executable to configure the computer system to: send a communication to the autonomous electric vehicle that causes the autonomous electric vehicle to travel to the first charging station location for charging.
 6. The computer system as recited in claim 1, wherein the vehicle location information comprises traffic information.
 7. The computer system as recited in claim 1, wherein the executable instructions for routing the vehicle selected from the one or more vehicles to the first charging station location for charging further include instructions that are executable to configure the computer system to: process, with a deep reinforcement learning algorithm, at least one of the following: the vehicle location information, the charging station locations, and the power distribution information.
 8. The computer system as recited in claim 7, wherein the executable instructions include instructions that are executable to configure the computer system to form a diamond-shape polyhedron for the deep reinforcement learning algorithm, wherein the diamond-shape polyhedron provides feasibility checks for solutions from the deep reinforcement learning algorithm.
 9. The computer system as recited in claim 1, wherein the executable instructions include instructions that are executable to configure the computer system to receive location information for one or more passengers hailing rides from the one or more vehicles.
 10. The computer system as recited in claim 9, wherein the executable instructions for routing the vehicle selected from the one or more vehicles to the first charging station location for charging further include instructions that are executable to configure the computer system to: process, with a deep reinforcement learning algorithm, at least one of the following: the vehicle location information, the charging station locations, the power distribution information, and the location information for the one or more passengers hailing rides.
 11. A computer-implemented method, executed on one or more processors, for real-time coordinated operation of power distribution systems and electric vehicles, comprising: accessing vehicle location information for one or more vehicles; accessing charging station locations for one or more charging stations within a power distribution system; accessing power distribution information describing voltage and/or current flow limits for the power distribution system; and routing a vehicle selected from the one or more vehicles to a first charging station location for charging, wherein the routing of the vehicle accounts for a current battery charge level of the vehicle and the power distribution information.
 12. The computer-implemented method as recited in claim 11, further comprising displaying a map, on a computer interface, wherein the map comprises a visual indication of a route to the first charging station location.
 13. The computer-implemented method as recited in claim 11, wherein the vehicle location information and the power distribution system are modelled with two interdependent graphs.
 14. The computer-implemented method as recited in claim 11, wherein at least one of the one or more vehicles comprises an autonomous electric vehicle.
 15. The computer-implemented method as recited in claim 14, wherein routing the vehicle selected from the one or more vehicles to the first charging station location for charging further comprises: sending a communication to the autonomous electric vehicle that causes the autonomous electric vehicle to travel to the first charging station location for charging.
 16. The computer-implemented method as recited in claim 11, wherein the vehicle location information comprises traffic information.
 17. The computer-implemented method as recited in claim 11, wherein routing the vehicle selected from the one or more vehicles to the first charging station location for charging further comprises processing, with a deep reinforcement learning algorithm, at least one of the following: the vehicle location information, the charging station locations, and the power distribution information.
 18. The computer-implemented method as recited in claim 17, further comprising forming a diamond-shape polyhedron for the deep reinforcement learning algorithm, wherein the diamond-shape polyhedron provides feasibility checks for solutions from the deep reinforcement learning algorithm.
 19. The computer-implemented method as recited in claim 11, further comprising configuring the computer system to receive location information for one or more passengers hailing rides from the one or more vehicles.
 20. The computer-implemented method as recited in claim 19, wherein routing the vehicle selected from the one or more vehicles to the first charging station location for charging further comprises: processing, with a deep reinforcement learning algorithm, at least one of the following: the vehicle location information, the charging station locations, the power distribution information, and the location information for the one or more passengers hailing rides. 